To answer the question regarding why the atomic radii of transition elements from chromium (Cr) to copper (Cu) are almost equal, we can break down the explanation into several steps:
### Step-by-Step Solution:
1. **Identify the Transition Elements**:
The first transition series includes the elements from Scandium (Sc) to Zinc (Zn), specifically: Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn.
2. **Understand the Electronic Configuration**:
The general electronic configuration for transition elements is given as \( ns^2 (n-1)d^{1-10} \). For example, chromium has the configuration \( [Ar] 4s^2 3d^4 \) and copper has \( [Ar] 4s^2 3d^{10} \).
3. **Effective Nuclear Charge (Z_eff)**:
As we move from left to right across the transition series, the number of protons in the nucleus increases, which leads to an increase in the effective nuclear charge (Z_eff). This generally causes a decrease in atomic size due to a stronger attraction between the nucleus and the electrons.
4. **Shielding Effect**:
The d-orbitals have a significant shielding effect. As we move from chromium to copper, the number of electrons in the d-orbitals increases, which enhances the shielding effect.
5. **Balance Between Z_eff and Shielding**:
From chromium to copper, the increase in Z_eff is counterbalanced by the increased shielding effect from the additional d-electrons. This balance results in the atomic radii remaining relatively constant.
6. **Comparison with Other Elements**:
Beyond copper, in the case of zinc, the shielding effect becomes greater than the Z_eff, leading to an increase in atomic size. However, from chromium to copper, the two effects are balanced, resulting in similar atomic radii.
7. **Conclusion**:
The atomic radii of transition elements from chromium to copper are almost equal because the increase in effective nuclear charge is balanced by the increased shielding effect from the d-electrons.
